Debt Policy, Corporate Taxes, and Discount Rates

This paper studies the valuation of assets with debt tax shields when debt policy is a general time-dependent function of the asset's unlevered cash flows, value, and history. In a continuous-time setting, it shows that the value of a project's debt tax shield satisfies a partial differential equation, which simplifies to an easily solved ordinary differential equation for most plausible debt policies. A large class of cases exhibits closed-form solutions for the value of a levered asset, the value of its tax shield, and the appropriate tax-adjusted cost of capital for discounting unlevered cash flows.